It’s a triangle. A triangle of numbers! Pascal did not create it…. The Chinese did. Blaise Pascal discovered all of the unique patterns in it.

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Presentation transcript:

It’s a triangle. A triangle of numbers! Pascal did not create it…. The Chinese did. Blaise Pascal discovered all of the unique patterns in it.

1 First we start off with a triangle of ones Then we add the left and right number together on the second row 2 Continue with this addition for each line

Just imagine 40 rows of a Triangle!

Each row has a reference number The very top is Row The sum of all the numbers in a row = 2 Row Number The sum of row 6 = 2 6 or 64 What is the sum of the eighth row? The answer is 2 8 or 256

Each number or element in a row has a reference number starting with the number 1. The first element is always element zero All of these 1’s are element 0 The next number in each row would be element 1 Let’s look at the 6 th row! Element 0 Element 1 Element 2 Element 3 Element 4 Element 5 Element 6

Let’s find the 3 rd element in 6 th row We’re at the 6 th rowNow let’s go to the 3 rd element

_______ Here is the 3 rd element in 6 th row Find 6 C 3 (nCr) or the 6 th row choose 3 rd element r!(n-r)! n! _______ 3×2×1(6-3)! 6×5×4×3×2×1 _____ 6(3)! 720 _____ 6(3×2×1) 720 _____ = 20 “!” is a factorial. Start with the number and multiply by every sequential number down to 1 5! = 5×4×3×2×1 or ! = 10×9×8×7×6×5×4×3×2×1 or 3,628,800

15! 5!(15-5)! _______ Let’s find the 5 element in the 15 th row We are finding nCr or 15 C 5. We are using our formula with n being the row and r being the element. 5 C 15 = nCr = r!(n-r)! n! _______ ( ) _______

Add together the two number above the 5 th spot. Go to the 15 th rowNow over to where the 5 th element would be 3003